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In the figure, AD = CD and AB = CB .

(i) Prove that Line BD bisects angle ADC (i.e. that line BD cuts angle ADC into two equal angles).

(ii) Prove that Line AC and Line DB are perpendicular.

Maplesnowy Mar 13, 2018

#1**+2 **

Since AD = CD

Then the angles opposite these sides are also equal

So angle DAC = angle DCA

And if AB = CB, then the angles opposite thes sides are also equal

So angle CAB = angle ACB

So angle DAC + angle CAB = angle DCA + angle ACB

So angle DAB = angle CDB

Then, by SAS....triangle DAB = triangle DCB

Then angle ADB = angle CDB.....so angle ADC is bisected

And angle DAC = angle DCA

AD = CD

And angle DAC = angle DCA

So....by ASA....triangle EAD = triangle ECD

So angle AED = angle CED

And, by Euclid.....a line standing upon a line that makes adjacent angles equal means that the lines are perpendicular....so AC and Db are perpendicular

CPhill Mar 13, 2018